#20018: init for endomorphism of projective subschemes fails
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Reporter: bhutz | Owner: bhutz
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-7.1
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers:
Authors: Ben Hutz | Work issues:
Report Upstream: N/A | Commit:
Branch: | bcb68d013dc8786c8f897f5d2b0c3329a93822a5
u/bhutz/ticket/20018 | Stopgaps:
Dependencies: |
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Changes (by {'newvalue': u'Ben Hutz', 'oldvalue': ''}):
* status: new => needs_review
* commit: => bcb68d013dc8786c8f897f5d2b0c3329a93822a5
* author: => Ben Hutz
Comment:
Since I didn't get any input from the sage-devel thread I went ahead an
implemented one possible correction to these issues. At this stage I
welcome comments on the solution.
The key points are as follows
- the actual coordinates of the map remain in the coordinate ring of the
ambient space (i.e., this is unchanged)
- if you initialize the map with variables from the coordinate ring of the
ambient space, they are not reduced modulo the defining ideal of the
subscheme (new behavior)
- if you initialize the map with variables from the coordinate ring of the
subscheme, they are in the quotient, so are reduced. (unchanged)
This allows initialization to work in more situations such as for the
problem in the description, but also corrects the weird behavior such as:
old behavior
{{{
sage: P.<x,y,z> = ProjectiveSpace(QQ,2)
sage: X=P.subscheme([x^2-y^2])
sage: H = End(X)
sage: f = H([x^2,y^2,z^2])
sage: f.multiplier(X([1,1]),1)
[0 2]
[0 2]
}}}
new behavior
{{{
sage: P.<x,y,z> = ProjectiveSpace(QQ,2)
sage: X=P.subscheme([x^2-y^2])
sage: H = End(X)
sage: f = H([x^2,y^2,z^2])
sage: f.multiplier(X([1,1]),1)
[2 0]
[0 2]
}}}
One consequence is the projective_embedding functionality in toric variety
seems to be programmed to expect the reduction. Consequently, I've had the
creation code use the quotient ring variables, so that behavior matches
the current doctests.
In a couple places in elliptic_curve/jacobian.py the morphism returned is
now in a slightly different form. This did not seem to big a difference,
so I just updated those doctests.
--
Ticket URL: <http://trac.sagemath.org/ticket/20018#comment:2>
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